On the Finite Element Method with Riesz Bases and Its Applications to Some Partial Differential Equations

Author

Fukuda, Nobuko ; Kinoshita, T. ; Kubo, T.

Author_Institution

Inst. of Math., Univ. of Tsukuba, Tsukuba, Japan

fYear

2013

fDate

15-17 April 2013

Firstpage

761

Lastpage

766

Abstract

In this paper, we will find the numerical solution of partial differential equations by using the finite element method with Riesz bases that are elevated from ortho normal bases. Especially for the two-dimensional cases, we also propose another way to solve a matrix-valued equation (Lyapunov equation). Moreover, we give the precise inverse formula for symmetric block tridiagonal Toeplitz matrices. To conclude, we present some numerical results that show the usefulness of the elevated bases.

Keywords

Lyapunov matrix equations; Toeplitz matrices; finite element analysis; inverse problems; partial differential equations; Lyapunov equation; Riesz bases; finite element method; inverse formula; matrix-valued equation; numerical solution; ortho normal bases; partial differential equations; symmetric block tridiagonal Toeplitz matrices; Boundary value problems; Elevators; Equations; Finite element analysis; Partial differential equations; Symmetric matrices; finite element method; wavelets;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Technology: New Generations (ITNG), 2013 Tenth International Conference on

Conference_Location

Las Vegas, NV

Print_ISBN

978-0-7695-4967-5

Type

conf

DOI

10.1109/ITNG.2013.121

Filename

6614407